model{
  ## Likelihood
  for(i in 1:N){
    y[i] ~ dpois(lambda[i])
    log(lambda[i]) <- mu[i]
    mu[i] <- beta0 + inprod(beta[],X[i,])+ b[X.b[i,1]]
  }     
  ## Priors 
  beta ~ dmnorm(mu.beta,tau.beta)  # multivariate Normal prior
  beta0 ~ dnorm(0,0.0001)
  
  for(j in 1:nb){
  b[j] ~ dnorm(0, tau) 
  }
  tau <- pow(sigma,-2)
  sigma ~ dunif(0,10)
}
